For the figures below, assume they are made of semicircles, quarter circles and squares. for each shape, find the area and perimeter. give your answer as a completely simplified exact value in terms of π (no approximations).

Part a) The area of the figure is

Part b) The perimeter of the figure is

Step-by-step explanation:

Step 1

Find the area of the figure

In this problem we have that

The figure ABC is the half of a square and the other figure is a semicircle

Find the area of the figure ABC

we have

The area of the half square ABC is equal to find the area of triangle ABC

so

Find the area of the semicircle

The area of the semicircle is equal to

we have that

substitute

The area of the figure is equal to

Step 2

Find the perimeter of the figure

The perimeter of the figure is equal to

we have

Applying Pythagoras theorem

Remember that

the circumference of a semicircle is equal to

The perimeter of the figure is equal to

Simplify